The Calabi flow with prescribed curvature on finite graphs
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911564394659840 |
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| author | Li, Yi Wang, Jie Yuan, Pingsan Zheng, Chao |
| author_facet | Li, Yi Wang, Jie Yuan, Pingsan Zheng, Chao |
| contents | In this paper, we investigate the prescribed curvature problem associated with a special Lin-Lu-Yau curvature on finite graphs of girth at least 6. We define the corresponding Calabi flow for this curvature type, and establish an equivalent characterization of the problem, namely, the solution to the Calabi flow exists globally in time and converges if and only if there exists a weight function that realizes the prescribed curvature. In particular, for constant curvature weights, we prove that the solution to the Calabi flow exists globally in time and converges under certain topological conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02632 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Calabi flow with prescribed curvature on finite graphs Li, Yi Wang, Jie Yuan, Pingsan Zheng, Chao Differential Geometry 52C26 In this paper, we investigate the prescribed curvature problem associated with a special Lin-Lu-Yau curvature on finite graphs of girth at least 6. We define the corresponding Calabi flow for this curvature type, and establish an equivalent characterization of the problem, namely, the solution to the Calabi flow exists globally in time and converges if and only if there exists a weight function that realizes the prescribed curvature. In particular, for constant curvature weights, we prove that the solution to the Calabi flow exists globally in time and converges under certain topological conditions. |
| title | The Calabi flow with prescribed curvature on finite graphs |
| topic | Differential Geometry 52C26 |
| url | https://arxiv.org/abs/2604.02632 |